Photon polarization states may be used to transmit securely a randomly generated key using quantum key distribution (QKD).
In one type of QKD, the sender (Alice) and the receiver (Bob) are connected by a quantum communication channel which allows quantum states to be transmitted. In addition they communicate via a classical channel.
Information sent from Alice to Bob is encoded in non-orthogonal states. Quantum indeterminacy means that these states cannot in general be measured by an eavesdropper (Eve) without disturbing the original state.
One QKD protocol uses two bases. A basis is defined by a pair of orthogonal states. Each basis is conjugate to the other base.
The usual polarization state pairs used are either the rectilinear basis of vertical (0°) and horizontal (90°), the diagonal basis of 45° and 135° or the circular basis of left- and right-handedness. Any two of these bases are conjugate to each other, and so any two can be used in the protocol
Alice creates a random bit (0 or 1) and then randomly selects one of her two bases (e.g. rectilinear or diagonal) to transmit it in. She then prepares a photon polarization state depending both on the information bit value and the selected basis. Alice then transmits to Bob a single photon in the state specified, using the quantum channel. This random bit creation and transmission is repeated to transmit all the information.
Bob does not know the basis the photons were encoded in. Bob selects a basis at random from the pair of bases used for encoding and uses it to measure the transmitted photon. He does this for each photon he receives, recording the time, measurement basis used and measurement result.
After Bob has measured all the photons, he communicates with Alice over the classical channel. Alice tells Bob the basis each photon was transmitted in, and Bob tells Alice the basis each photon was measured in. They both discard photon measurements (bits) where Bob used a different basis.
To check for the presence of eavesdropping Alice and Bob now compare a certain subset of their remaining bit strings. If Eve has measured any of the photons' polarizations, errors are introduced into Bobs' measurements. If the errors are less than a threshold then the quantum channel may be considered secure.
A modification to this protocol is described in “Reference frame independent quantum key distribution” by Laing et al, 4 Mar. 2010, Phys Rev A 82, 012304. This paper describes a theoretical frame independent quantum key distribution scheme.
The sender (Alice) and the receiver (Bob) are notionally connected by a free space quantum communication channel which allows quantum states to be transmitted. In addition they communicate via a classical channel.
This protocol uses three bases. A basis is defined by a pair of orthogonal states. Each basis is conjugate to the other bases.
The usual polarization bases used are the rectilinear basis of vertical (0°) and horizontal (90°), the diagonal basis of 45° and 135° and the circular basis of left- and right-handedness.
Alice creates a random bit (0 or 1) and then randomly selects one of her three bases (e.g. rectilinear, diagonal, circular) to transmit it in. She then prepares a photon polarization state depending both on the bit value and the selected basis. Alice then transmits to Bob a single photon in the state specified, using the quantum channel. This random bit creation and transmission is repeated.
Bob does not know the basis the photons were encoded in. Bob selects a basis at random from the three bases used for encoding and uses it to measure the transmitted photon. He does this for each photon he receives, recording the time, measurement basis used and measurement result.
After Bob has measured all the photons, he communicates with Alice over the classical channel. Alice tells Bob the basis each photon was sent in, and Bob tells Alice the basis each was measured in.
They both define photon measurements (bits) as either ‘matched’ or unmatched’. Matching occurs when Alice and Bob have used the same basis for the same bit.
One of the three bases, the circular basis, is considered to be invariant and unaffected by relative movement of Bob and Alice.
Alice and Bob share as common knowledge which basis is the ‘invariant’ basis. They both use the matched bits that were measured using the invariant basis and use them as a shared key (raw key). The other bits sent/measured using the non-invariant bases may be used to calculate a statistical expression to estimate Eve's information.